0.0505 Repeating as a Fraction
Introduction
Repeating decimals, also known as recurring decimals, are a type of decimal number that has a sequence of digits that repeats indefinitely. One such example is 0.0505, which has a repeating pattern of 05. But have you ever wondered what this repeating decimal represents as a fraction? In this article, we'll explore how to convert 0.0505 repeating as a fraction.
Converting Repeating Decimals to Fractions
To convert a repeating decimal to a fraction, we can use a simple trick. Let's define the repeating decimal as x:
x = 0.0505...
We can multiply both sides of the equation by 100, since the repeating pattern has two digits:
100x = 5.05...
Now, subtract the original equation from the new equation:
100x - x = 5.05 - 0.0505 99x = 4.99
Next, divide both sides of the equation by 99:
x = 4.99 / 99 x = 499 / 9900
Simplifying the Fraction
We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 99.
x = 499 / 9900 = 5 / 100 = 1 / 20
And there you have it! The repeating decimal 0.0505 represents the fraction 1/20.
Conclusion
Repeating decimals might seem complex, but they can be easily converted to fractions using a simple trick. In this case, we've seen that 0.0505 repeating is equivalent to the fraction 1/20. This conversion can be useful in various mathematical applications, such as algebra, geometry, and more.
